Bunuel wrote:
What is the value of x?
(1) |x + 9| = 2x.
The left hand side is an absolute value, so it cannot be negative, thus the right hand side also cannot be negative, which means that x is positive or 0. If\(x \geq 0\) , then x + 9 > 0, thus |x + 9| = x + 9. So, we'd have that x + 9 = 2x. Solving gives x = 9. Sufficient.
(2) |2x − 9| = x.
2x - 9 = x --> x = 9. Plug back to verify this solution: |2*9 - 9| = 9 --> OK;
2x - 9 = -x --> x = 3. Plug back to verify this solution: |2*3 - 9| = 3
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